Devi Shailputri is worshiped just after the Ghatasthapana process. You may about it here:
Ghatasthapana Muhurat Rules & Puja Vidhi For The First Day Of Navratri
Mata Shailputri looks like this:
• Half Moon on the forehead
• Trident in right hand
• Lotus in left hand
• Mounted on Nandi, the bull
Shailaputri is a Sanskrit name, which means - the daughter of the mountain (Shaila = Mountain, Putri = Daughter). As the legend goes, Maa Durga had taken birth in the home of the Parvat Raj Himalaya (King of the Himalayas). Hence, this incarnation of hers got the name Shailputri. The name of the King of the Himalayas was Hemavana. Hence, she also got the name Hemavati.
In her previous birth, she was the consort of Shiva and daughter of Daksha. So, she also has names like Sati, Bhavani. Once, Daksha organized a big Yajna event. He didn’t invite Shiva. But, Sati couldn’t resist it and she arrived there. During the Yajna, Daksha insulted Shiva. She could not take it and jumped into the fire of Yajna. Later, she took birth in the home of Mountain Lord as Parvati (also Hemavati) and married Lord Shiva again.
As she rides on the bull, she is also known as Vrisharudha. It is a Sankrit term made of 2 words: Vrisha = bull and Arudha = to be placed upon.
Goddess Shailputri governs the planet Moon in astrology. Worshiping her can eliminate all the bad effects of Moon.
ॐ देवी शैलपुत्र्यै नमः॥
वन्दे वाञ्छितलाभाय चन्द्रार्धकृतशेखराम्।
वृषारुढां शूलधरां शैलपुत्रीं यशस्विनीम्॥
Stuti: या देवी सर्वभूतेषु माँ शैलपुत्री रूपेण संस्थिता। नमस्तस्यै नमस्तस्यै नमस्तस्यै नमो नम:॥